5/7x+1/3x=21

Solution for 5/7x+1/3x=21 equation:

5/7x+1/3x=21

We move all terms to the left:

5/7x+1/3x-(21)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


15x/21x^2+7x/21x^2-21=0

We multiply all the terms by the denominator


15x+7x-21*21x^2=0

We add all the numbers together, and all the variables

22x-21*21x^2=0

Wy multiply elements

-441x^2+22x=0

a = -441; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-441)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-441}=\frac{-44}{-882}
=22/441
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-441}=\frac{0}{-882}
=0
$